The film's title is a cryptic reference to the men in the film hired to smuggle 48 nuclear weapons components into the United States as part of a secret war game and the unexpected 49th man, using the war game as cover, smuggling in a real atomic bomb as part of a plot to destroy an American city.

After a fatal car crash in Lordsburg, New Mexico, investigators find a mysterious machine component that they turn over to the nearby Los Alamos National Laboratory for identification.

While in Marseilles, he learns that civilians Margo Wayne (Suzanne Dalbert) and her husband Leo Wayne (Peter Marshall) are working with clarinet player Buzz Olin (Richard Avonde) and an unknown member of the submarine's crew to smuggle the parts in special metal cases built by Pierre Neff (George Dee).

They have used Neff to construct 4 cases, in addition to the 48 ordered by the naval officers, and smuggled their own portable nuclear weapon into the United States.

With less than 48 hours before the bomb's scheduled detonation at 3 p.m. on Tuesday, Williams and his team track Buzz Olin and the Waynes to the San Francisco area.